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Groupon shares rose more than 7% to a new 52-week high Thursday after an analyst upgrade stoked optimism that the online deals company will grow faster and more profitably soon.

Jordan Rohan, an analyst at Stifel Nicolaus, upgraded Groupon to buy from hold and slapped a $16 price target on the stock after a recent trip to the company's Chicago headquarters.

"While the company has not yet shown a big acceleration in total growth rate, the acceleration of growth is likely soon, perhaps this quarter," Rohan wrote in a note to investors. "Importantly, when that accelerating growth materializes, we believe it will also come with higher margins."

Groupon ousted co-founder and CEO Andrew Mason earlier this year and the company's chairman Eric Lefkofsky took over. Even before Mason left, Groupon shares had begun to rebound from a record low late in 2012.

Groupon used to blast daily deals on local goods and services to millions of subscribers via email, but the company has been reducing its reliance on this, in favor of a big pool of online vouchers and deals that can be searched by consumers.

This has begun to pay off. The number of unique visitors coming to Groupon's website has jumped this year, while its closest rival LivingSocial has seen minimal growth, Rohan noted, citing comScore data.

Meanwhile, Lefkofsky is trying to make Groupon's operations more efficient, which could help profit margins, Rohan said.

Groupon shares were up 7.6% to $12.43 in morning trading Thursday. The stock high a 52-week high of $12.45 earlier in the day.